In the remainder of this section we will study in some detail an example: we will see that
the bundle gerbes of Murray [1]} provide
interesting examples of twisted cartesian products in the category
\(s{K}\)  of simplicial spaces (i.e. when \(B\)  is a point).
Recall from [1]} that a bundle gerbe on a space
\(M\)  consists of a map \(\pi \colon Y_0\rightarrow M\)  which admits local sections
together with a \(S^1\)  principal bundle \(Y_1\rightarrow Y_0^{[2]}\) . The \(S^1\)  bundle
\(Y_1\)  is required to have an associative product,
in other words there is an isomorphism of \(S^1\)  bundles over \(Y_0^{[3]}\)  which on fibers takes the form
\((Y_1)_{(y_1,y_2)}\otimes (Y_1)_{(y_2,y_3)}\rightarrow (Y_1)_{(y_1,y_3)}\) 
